Question

# Consider a game in which a red die and a blue die are rolled. Let xR...

Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die. (a) The probability distribution of xR is as follows. xR p(xR) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6

Find the mean, variance, and standard deviation of xR. (Round your answers to three decimal places.)

Mean = Variance = Standard deviation =

(b) What are the values of the mean, variance, and standard deviation of xB? You should be able to answer this question without doing any additional calculations. (Round your answers to three decimal places.) Mean = Variance = Standard deviation =

(c) Suppose that you are offered a choice of the following two games. Game 1: Costs \$7 to play, and you win y1 dollars, where y1 = xR + xB. Game 2: Doesn't cost anything to play initially, but you "win" 2y2 dollars, where y2 = xR - xB. If y2 is negative, you must pay that amount; if it is positive, you receive that amount. For Game 1, the net amount won in a game is w1 = y1 - 7 = xR + xB - 7. What are the mean and standard deviation of w1? (Round your answers to three decimal places.) Mean = Standard deviation = (d)

For Game 2, the net amount won in a game is w2 = 2y2 = 2(xR - xB). What are the mean and standard deviation of w2? (Round your answers to three decimal places.) Mean = Standard deviation = (e)

Based on your answers to Parts (c) and (d), which game would you choose if you are quite a risky person? Game 2 Game 1

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